Asymptotically Lifshitz spacetimes with universal horizons in $(1 + 2)$ dimensions

TL;DR

This paper explores conditions for Lifshitz spacetimes with universal horizons in 2+1 dimensional Horava gravity, constructs explicit solutions, and demonstrates their thermodynamic properties, advancing holographic understanding in non-AdS contexts.

Contribution

It derives conditions for universal horizons in Lifshitz spacetimes within Horava gravity and provides explicit numerical solutions with thermodynamic analysis.

Findings

Universal horizons exist under specific conditions in 2+1D Lifshitz spacetimes.

Constructed explicit regular solutions numerically.

First law of thermodynamics holds at the universal horizon.

Abstract

Horava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two derivative Horava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z=2 in 1+2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti-de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.